PHYS-222 Worksheet 9 for Section 25 & 36 Problem 9-1

PHYS-222 Worksheet 9 for Section 25 & 36
TA: Yang Li, [email protected]
October 7, 2012
Problem 9-1
~ r) in the following cases:
Use Ampere’s law to calculate the magnetic field B(~
a. a long straight wire carries electric current I (the transverse diameter of the wire can be neglected);
key: B = µ2πr
b. two long wires both carry electric current I in the same direction. The separation distance between
µ0 I
µ0 I
two wires is d (the transverse diameter of the wire can be neglected); key: B = 2π(d/2+r)
+ 2π(d/2−r)
c. a long cylindrical wire carries uniform electric current I. The radius of the wire is a. Calculate magnetic
µ0 Ir
field both inside and ourside the wire; key: B = µ2πr
(r > a), B = 2πa
(r ≤ 0)
d. a long cylindrical solenoid carries electric current I. The length of the solenoid is L and the number of
coils is N . The radius of the solenoid is a; Find the magnetic field both inside and outside the solenoid.
key: B = N
(r ≤ a), B = 0 (r > a)
L µ0 I
e. a very large conducting sheet carries uniform electric current. The current per unit length is σ. key:
B = µ20 σ
Problem 9-2
A current I flows in a plane rectangular current loop with height w and horizontal sides b. The loop is placed
~ in such a way that the sides of length w are perpendicular to B
~ (Figure (a))
into a uniform magnetic field B
~ (Figure (b)) . Calculate τ , the magnitude of
, and there is an angle θ between the sides of length b and B
the torque about the vertical axis of the current loop due to the interaction of the current through the loop
with the magnetic field. key: τ = BIwb sin θ